Robust energy-to-peak control for Markov jump system with multiple pure time delays

Abstract

This paper investigates the robust energy-to-peak stability analysis and controller design for Markov jump system with multiple pure time delays. The aim is to get some sufficient conditions such that the controlled system is asymptotically stable with an anti-disturbance performance. Firstly, according to the system transformation, the Markov jump multiple pure time delays system is transformed into a new description, which includes a non-time-delay item and some integral items. Secondly, according to Lyapunov stability theory and linear matrix inequality (LMI) technique, the sufficient theorems are achieved for the Markov jump multiple pure time delays system to be energy-to-peak stability and stabilisation. If those theorems are solvable, controllers can be obtained such that the controlled systems are stable and the peak-values of the controlled outputs are constrained for any energy-bounded external disturbance inputs. Moreover, the uncertain cases are considered, and the robust stability conditions are achieved. Finally, examples are given, and the effectiveness of the obtained methods is illustrated.